# Translation

• May 20th 2010, 12:21 PM
Mukilab
Translation
How does one 'Describe fully a single translation'?

My object has been reflected twice, do I just say 'reflected on x=_ then on y=_'?
• May 20th 2010, 10:29 PM
Combining two reflections
Hello Mukilab
Quote:

Originally Posted by Mukilab
How does one 'Describe fully a single translation'?

My object has been reflected twice, do I just say 'reflected on x=_ then on y=_'?

Are you sure the question says 'a single translation'? The combined transformation will be a translation only if the two mirror-lines are parallel. And from what you say about '\$\displaystyle x =... \$' and '\$\displaystyle y =...\$', it sounds as if they aren't.

Does the question say 'Describe fully a single transformation ...'?

When one reflection is followed by a second reflection in mirror-lines that are not parallel, this is equivalent to a rotation, whose centre is at the point where the mirror-lines meet, through twice the angle between them.

It sounds as if your mirror-lines are at right-angles, so the rotation will be through a half-turn.

Does that help to answer your question?

• May 21st 2010, 08:27 AM
Mukilab
It can't just be a rotation, it doesn't make sense.

It is 'single transformation'

Here are the coordinates of the three triangles
A= 0,3 1,3 and 1,5
B= 3,0 3,1 and 5,1
C= 5,3 6,3 and 5,5

Describe the translation of A onto B. Is this a reflection around line y=x?
• May 21st 2010, 12:37 PM
Hello Mukilab
Quote:

Originally Posted by Mukilab
It can't just be a rotation, it doesn't make sense.

It is 'single transformation'

Here are the coordinates of the three triangles
A= 0,3 1,3 and 1,5
B= 3,0 3,1 and 5,1
C= 5,3 6,3 and 5,5

Describe the translation of A onto B. Is this a reflection around line y=x?

Again, you have used the word 'translation' when you meant 'transformation'.

I was guessing what the answer might be, based on the incomplete information you gave me in your first post. You are right: the transformation that maps A onto B is a reflection in the line \$\displaystyle y = x\$.

B is then mapped onto C by a rotation through \$\displaystyle 90^o\$ anticlockwise, centre \$\displaystyle (3,3)\$.

The single transformation that maps A onto C is a reflection in the line \$\displaystyle x = 3\$.